Abstract

A simple imaging method for direct determination of single-molecule orientations is presented that uses a wide-field epifluorescence microscope and a sensitive CCD camera. Imaging is performed with slight defocusing of the optics, allowing for direct determination of single-molecule orientation based on the characteristic intensity distribution of the defocused images. Exact wave-optical calculations of these defocused images are presented and are in good agreement with the measurements. These calculations represent what is to the authors’ knowledge the first complete wave-optical modeling of defocused imaging of dipole emitters at an interface; the peculiarities of dipole emission at an interface and the vector effects of that emission and of imaging with a high-numerical-aperture objective are taken into account.

© 2003 Optical Society of America

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2001 (5)

C. Tietz, F. Jelezko, U. Gerken, S. Schuler, A. Schubert, H. Rogl, and J. Wrachtrup, “Single-molecule spectroscopy on the light-harvesting complex II of higher plants,” Biophys. J. 81, 556–562 (2001).
[CrossRef] [PubMed]

L. A. Deschenes and D. A. Van den Bout, “Single-molecule studies of heterogeneous dynamics in polymer melts near the glass transition,” Science 292, 233–234 (2001).
[CrossRef]

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86, 5251–5254 (2001).
[CrossRef] [PubMed]

J. T. Fourkas, “Rapid determination of the three-dimensional orientation of single molecules,” Opt. Lett. 26, 211–213 (2001).
[CrossRef]

M. A. Lieb and A. J. Meixner, “A high numerical aperture parabolic mirror as imaging device for confocal microscopy,” Opt. Express 8, 458–474 (2001), http://www.opticsexpress.org.
[CrossRef] [PubMed]

2000 (4)

J. Enderlein, “Theoretical study of detecting a dipole emitter through an objective with high numerical aperture,” Opt. Lett. 25, 634–636 (2000).
[CrossRef]

B. Sick, B. Hecht, and L. Novotny, “Orientational imaging of single molecules by annular illumination,” Phys. Rev. Lett. 85, 4482–4485 (2000).
[CrossRef] [PubMed]

W. Trabesinger, A. Renn, B. Hecht, U. P. Wild, A. Montali, P. Smith, and C. Weder, “Single-molecule imaging revealing the deformation-induced formation of a molecular polymer blend,” J. Phys. Chem. B 104, 5221–5224 (2000).
[CrossRef]

N. F. Van Hulst, J. A. Veerman, M. F. García-Parajó, and L. Kuipers, “Analysis of individual (macro)molecules and proteins using near-field optics,” J. Chem. Phys. 112, 7790–7810 (2000).
[CrossRef]

1999 (9)

K. Kinosita, “Real time imaging of rotating molecular machines,” FASEB J. 13, S201–S208 (1999).

J. A. Veerman, M. F. Garcia-Parajo, L. Kuipers, and N. F. Van Hulst, “Single-molecule mapping of the optical field distribution of probes for near-field microscopy,” J. Microsc. (Oxford) 194, 477–482 (1999).
[CrossRef]

J. A. Veerman, S. A. Levi, F. C. J. M. Van Veggel, D. N. Reinhoudt, and N. F. Van Hulst, “Near-field scanning optical microscopy of single fluorescent dendritic molecules,” J. Phys. Chem. A 103, 11264–11270 (1999).
[CrossRef]

M. F. Garcia-Parajo, J. A. Veerman, G. M. J. Segers-Nolten, B. G. De Grooth, J. Greve, and N. F. Van Hulst, “Visualizing individual green fluorescent proteins with a near-field optical microscope,” Cytometry 36, 239–246 (1999).
[CrossRef] [PubMed]

A. P. Bartko and R. M. Dickson, “Three-dimensional orientations of polymer-bound single molecules,” J. Phys. Chem. B 103, 3053–3056 (1999).
[CrossRef]

A. P. Bartko and R. M. Dickson, “Imaging three-dimensional single-molecule orientations,” J. Phys. Chem. B 103, 11237–11241 (1999).
[CrossRef]

R. A. Farrer, M. J. R. Previte, C. E. Olson, L. A. Peyser, J. T. Fourkas, and P. T. C. So, “Single-molecule detection with a two-photon fluorescence microscope with fast-scanning capabilities and polarization sensitivity,” Opt. Lett. 24, 1832–1834 (1999).
[CrossRef]

J. Enderlein, T. Ruckstuhl, and S. Seeger, “Highly efficient optical detection of surface-generated fluorescence,” Appl. Opt. 38, 724–732 (1999).
[CrossRef]

T. Ha, T. A. Laurence, D. S. Chemla, and S. Weiss, “Polarization spectroscopy of single fluorescent molecules,” J. Phys. Chem. B 103, 6839–6850 (1999).
[CrossRef]

1998 (4)

R. M. Dickson, D. J. Norris, and W. E. Moerner, “Simultaneous imaging of individual molecules aligned both parallel and perpendicular to the optic axis,” Phys. Rev. Lett. 81, 5322–5325 (1998).
[CrossRef]

K. Kinosita, “Linear and rotary molecular motors,” Adv. Exp. Med. Biol. 453, 5–14 (1998).
[CrossRef]

J. Hofkens, W. Verheijen, R. Shulka, H. W. Schryver, and F. C. De, “Detection of a single dendrimer macromolecule with a fluorescent dihydropyrrolopurroledione (DPP) core embedded in a thin polystyrene film,” Macromolecules 32, 4493–4497 (1998).
[CrossRef]

D. M. Warshaw, E. Hayes, D. Gaffney, A. M. Lauzon, J. R. Wu, G. Kennedy, K. Trybus, S. Lowey, and C. Berger, “Myosin conformational states determined by single fluorophore polarization,” Proc. Natl. Acad. Sci. (USA) 95, 8034–8039 (1998).
[CrossRef]

1997 (3)

A. G. T. Ruiter, J. A. Veerman, M. F. Garcia-Parajo, and N. F. Van Hulst, “Single-molecule rotational and translational diffusion observed by near-field scanning optical microscopy,” J. Phys. Chem. A 101, 7318–7323 (1997).
[CrossRef]

J. Jasny and J. Sepiol, “Single molecules observed by immersion mirror objective: a novel method of finding the orientation of a radiating dipole,” Chem. Phys. Lett. 273, 439–443 (1997).
[CrossRef]

J. Sepiol, J. Jasny, J. Keller, and U. P. Wild, “Single molecules observed by immersion mirror objective: the orientation of terrylene molecules via the direction of its transition dipole-moment,” Chem. Phys. Lett. 273, 444–448 (1997).
[CrossRef]

1996 (6)

M. A. Bopp, A. J. Meixner, G. Tarrach, I. Zschokke-Gränacher, and L. Novotny, “Direct imaging of single molecule diffusion in a solid polymer host,” Chem. Phys. Lett. 263, 721–726 (1996).
[CrossRef]

T. Ha, T. Enderle, D. S. Chemla, P. R. Selvin, and S. Weiss, “Single-molecule dynamics studied by polarization modulation,” Phys. Rev. Lett. 77, 3979–3982 (1996).
[CrossRef] [PubMed]

T. Ha, T. Enderle, D. S. Chemla, and S. Weiss, “Dual-molecule spectroscopy: molecular rulers for the study of biological macromolecules,” IEEE J. Sel. Top. Quantum Electron. 2, 1115–1128 (1996).
[CrossRef]

J. K. Trautman and J. J. Macklin, “Time-resolved spectroscopy of single molecules using near-field and far-field optics,” Chem. Phys. 205, 221–229 (1996).
[CrossRef]

J. J. Macklin, J. K. Trautman, T. D. Harris, and L. E. Brus, “Imaging and time-resolved spectroscopy of single molecules at an interface,” Science 272, 255–258 (1996).
[CrossRef]

A. Ishijima, H. Kojima, H. Higuchi, Y. Harada, R. Vale, T. Funatsu, and T. Yanagida, “Multiple-molecule and single-molecule analysis of the actomyosin motor by nanometer piconewton manipulation with a microneedle: unitary steps and forces,” Biophys. J. 70, 383–400 (1996).
[CrossRef] [PubMed]

1994 (1)

W. P. Ambrose, P. M. Goodwin, J. C. Martin, and R. A. Keller, “Single-molecule detection and photochemistry of a surface using near-field optical excitation,” Phys. Rev. Lett. 72, 160–163 (1994).
[CrossRef] [PubMed]

1991 (1)

K. Kinosita, H. Itoh, S. Ishiwata, K. Hirano, T. Nishizaka, and T. Hayakawa, “Dual-view microscopy with a single camera: real-time imaging of molecular orientations and calcium,” J. Cell Biol. 115, 67–73 (1991).
[CrossRef] [PubMed]

1987 (1)

1959 (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London Ser. A 235, 358–379 (1959).
[CrossRef]

Ambrose, W. P.

W. P. Ambrose, P. M. Goodwin, J. C. Martin, and R. A. Keller, “Single-molecule detection and photochemistry of a surface using near-field optical excitation,” Phys. Rev. Lett. 72, 160–163 (1994).
[CrossRef] [PubMed]

Axelrod, D.

Bartko, A. P.

A. P. Bartko and R. M. Dickson, “Imaging three-dimensional single-molecule orientations,” J. Phys. Chem. B 103, 11237–11241 (1999).
[CrossRef]

A. P. Bartko and R. M. Dickson, “Three-dimensional orientations of polymer-bound single molecules,” J. Phys. Chem. B 103, 3053–3056 (1999).
[CrossRef]

Berger, C.

D. M. Warshaw, E. Hayes, D. Gaffney, A. M. Lauzon, J. R. Wu, G. Kennedy, K. Trybus, S. Lowey, and C. Berger, “Myosin conformational states determined by single fluorophore polarization,” Proc. Natl. Acad. Sci. (USA) 95, 8034–8039 (1998).
[CrossRef]

Beversluis, M. R.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86, 5251–5254 (2001).
[CrossRef] [PubMed]

Bopp, M. A.

M. A. Bopp, A. J. Meixner, G. Tarrach, I. Zschokke-Gränacher, and L. Novotny, “Direct imaging of single molecule diffusion in a solid polymer host,” Chem. Phys. Lett. 263, 721–726 (1996).
[CrossRef]

Brown, T. G.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86, 5251–5254 (2001).
[CrossRef] [PubMed]

Brus, L. E.

J. J. Macklin, J. K. Trautman, T. D. Harris, and L. E. Brus, “Imaging and time-resolved spectroscopy of single molecules at an interface,” Science 272, 255–258 (1996).
[CrossRef]

Chemla, D. S.

T. Ha, T. A. Laurence, D. S. Chemla, and S. Weiss, “Polarization spectroscopy of single fluorescent molecules,” J. Phys. Chem. B 103, 6839–6850 (1999).
[CrossRef]

T. Ha, T. Enderle, D. S. Chemla, P. R. Selvin, and S. Weiss, “Single-molecule dynamics studied by polarization modulation,” Phys. Rev. Lett. 77, 3979–3982 (1996).
[CrossRef] [PubMed]

T. Ha, T. Enderle, D. S. Chemla, and S. Weiss, “Dual-molecule spectroscopy: molecular rulers for the study of biological macromolecules,” IEEE J. Sel. Top. Quantum Electron. 2, 1115–1128 (1996).
[CrossRef]

De, F. C.

J. Hofkens, W. Verheijen, R. Shulka, H. W. Schryver, and F. C. De, “Detection of a single dendrimer macromolecule with a fluorescent dihydropyrrolopurroledione (DPP) core embedded in a thin polystyrene film,” Macromolecules 32, 4493–4497 (1998).
[CrossRef]

De Grooth, B. G.

M. F. Garcia-Parajo, J. A. Veerman, G. M. J. Segers-Nolten, B. G. De Grooth, J. Greve, and N. F. Van Hulst, “Visualizing individual green fluorescent proteins with a near-field optical microscope,” Cytometry 36, 239–246 (1999).
[CrossRef] [PubMed]

Deschenes, L. A.

L. A. Deschenes and D. A. Van den Bout, “Single-molecule studies of heterogeneous dynamics in polymer melts near the glass transition,” Science 292, 233–234 (2001).
[CrossRef]

Dickson, R. M.

A. P. Bartko and R. M. Dickson, “Imaging three-dimensional single-molecule orientations,” J. Phys. Chem. B 103, 11237–11241 (1999).
[CrossRef]

A. P. Bartko and R. M. Dickson, “Three-dimensional orientations of polymer-bound single molecules,” J. Phys. Chem. B 103, 3053–3056 (1999).
[CrossRef]

R. M. Dickson, D. J. Norris, and W. E. Moerner, “Simultaneous imaging of individual molecules aligned both parallel and perpendicular to the optic axis,” Phys. Rev. Lett. 81, 5322–5325 (1998).
[CrossRef]

Enderle, T.

T. Ha, T. Enderle, D. S. Chemla, and S. Weiss, “Dual-molecule spectroscopy: molecular rulers for the study of biological macromolecules,” IEEE J. Sel. Top. Quantum Electron. 2, 1115–1128 (1996).
[CrossRef]

T. Ha, T. Enderle, D. S. Chemla, P. R. Selvin, and S. Weiss, “Single-molecule dynamics studied by polarization modulation,” Phys. Rev. Lett. 77, 3979–3982 (1996).
[CrossRef] [PubMed]

Enderlein, J.

Farrer, R. A.

Fourkas, J. T.

Funatsu, T.

A. Ishijima, H. Kojima, H. Higuchi, Y. Harada, R. Vale, T. Funatsu, and T. Yanagida, “Multiple-molecule and single-molecule analysis of the actomyosin motor by nanometer piconewton manipulation with a microneedle: unitary steps and forces,” Biophys. J. 70, 383–400 (1996).
[CrossRef] [PubMed]

Gaffney, D.

D. M. Warshaw, E. Hayes, D. Gaffney, A. M. Lauzon, J. R. Wu, G. Kennedy, K. Trybus, S. Lowey, and C. Berger, “Myosin conformational states determined by single fluorophore polarization,” Proc. Natl. Acad. Sci. (USA) 95, 8034–8039 (1998).
[CrossRef]

Garcia-Parajo, M. F.

M. F. Garcia-Parajo, J. A. Veerman, G. M. J. Segers-Nolten, B. G. De Grooth, J. Greve, and N. F. Van Hulst, “Visualizing individual green fluorescent proteins with a near-field optical microscope,” Cytometry 36, 239–246 (1999).
[CrossRef] [PubMed]

J. A. Veerman, M. F. Garcia-Parajo, L. Kuipers, and N. F. Van Hulst, “Single-molecule mapping of the optical field distribution of probes for near-field microscopy,” J. Microsc. (Oxford) 194, 477–482 (1999).
[CrossRef]

A. G. T. Ruiter, J. A. Veerman, M. F. Garcia-Parajo, and N. F. Van Hulst, “Single-molecule rotational and translational diffusion observed by near-field scanning optical microscopy,” J. Phys. Chem. A 101, 7318–7323 (1997).
[CrossRef]

García-Parajó, M. F.

N. F. Van Hulst, J. A. Veerman, M. F. García-Parajó, and L. Kuipers, “Analysis of individual (macro)molecules and proteins using near-field optics,” J. Chem. Phys. 112, 7790–7810 (2000).
[CrossRef]

Gerken, U.

C. Tietz, F. Jelezko, U. Gerken, S. Schuler, A. Schubert, H. Rogl, and J. Wrachtrup, “Single-molecule spectroscopy on the light-harvesting complex II of higher plants,” Biophys. J. 81, 556–562 (2001).
[CrossRef] [PubMed]

Goodwin, P. M.

W. P. Ambrose, P. M. Goodwin, J. C. Martin, and R. A. Keller, “Single-molecule detection and photochemistry of a surface using near-field optical excitation,” Phys. Rev. Lett. 72, 160–163 (1994).
[CrossRef] [PubMed]

Greve, J.

M. F. Garcia-Parajo, J. A. Veerman, G. M. J. Segers-Nolten, B. G. De Grooth, J. Greve, and N. F. Van Hulst, “Visualizing individual green fluorescent proteins with a near-field optical microscope,” Cytometry 36, 239–246 (1999).
[CrossRef] [PubMed]

Ha, T.

T. Ha, T. A. Laurence, D. S. Chemla, and S. Weiss, “Polarization spectroscopy of single fluorescent molecules,” J. Phys. Chem. B 103, 6839–6850 (1999).
[CrossRef]

T. Ha, T. Enderle, D. S. Chemla, P. R. Selvin, and S. Weiss, “Single-molecule dynamics studied by polarization modulation,” Phys. Rev. Lett. 77, 3979–3982 (1996).
[CrossRef] [PubMed]

T. Ha, T. Enderle, D. S. Chemla, and S. Weiss, “Dual-molecule spectroscopy: molecular rulers for the study of biological macromolecules,” IEEE J. Sel. Top. Quantum Electron. 2, 1115–1128 (1996).
[CrossRef]

Harada, Y.

A. Ishijima, H. Kojima, H. Higuchi, Y. Harada, R. Vale, T. Funatsu, and T. Yanagida, “Multiple-molecule and single-molecule analysis of the actomyosin motor by nanometer piconewton manipulation with a microneedle: unitary steps and forces,” Biophys. J. 70, 383–400 (1996).
[CrossRef] [PubMed]

Harris, T. D.

J. J. Macklin, J. K. Trautman, T. D. Harris, and L. E. Brus, “Imaging and time-resolved spectroscopy of single molecules at an interface,” Science 272, 255–258 (1996).
[CrossRef]

Hayakawa, T.

K. Kinosita, H. Itoh, S. Ishiwata, K. Hirano, T. Nishizaka, and T. Hayakawa, “Dual-view microscopy with a single camera: real-time imaging of molecular orientations and calcium,” J. Cell Biol. 115, 67–73 (1991).
[CrossRef] [PubMed]

Hayes, E.

D. M. Warshaw, E. Hayes, D. Gaffney, A. M. Lauzon, J. R. Wu, G. Kennedy, K. Trybus, S. Lowey, and C. Berger, “Myosin conformational states determined by single fluorophore polarization,” Proc. Natl. Acad. Sci. (USA) 95, 8034–8039 (1998).
[CrossRef]

Hecht, B.

B. Sick, B. Hecht, and L. Novotny, “Orientational imaging of single molecules by annular illumination,” Phys. Rev. Lett. 85, 4482–4485 (2000).
[CrossRef] [PubMed]

W. Trabesinger, A. Renn, B. Hecht, U. P. Wild, A. Montali, P. Smith, and C. Weder, “Single-molecule imaging revealing the deformation-induced formation of a molecular polymer blend,” J. Phys. Chem. B 104, 5221–5224 (2000).
[CrossRef]

Hellen, E. H.

Higuchi, H.

A. Ishijima, H. Kojima, H. Higuchi, Y. Harada, R. Vale, T. Funatsu, and T. Yanagida, “Multiple-molecule and single-molecule analysis of the actomyosin motor by nanometer piconewton manipulation with a microneedle: unitary steps and forces,” Biophys. J. 70, 383–400 (1996).
[CrossRef] [PubMed]

Hirano, K.

K. Kinosita, H. Itoh, S. Ishiwata, K. Hirano, T. Nishizaka, and T. Hayakawa, “Dual-view microscopy with a single camera: real-time imaging of molecular orientations and calcium,” J. Cell Biol. 115, 67–73 (1991).
[CrossRef] [PubMed]

Hofkens, J.

J. Hofkens, W. Verheijen, R. Shulka, H. W. Schryver, and F. C. De, “Detection of a single dendrimer macromolecule with a fluorescent dihydropyrrolopurroledione (DPP) core embedded in a thin polystyrene film,” Macromolecules 32, 4493–4497 (1998).
[CrossRef]

Ishijima, A.

A. Ishijima, H. Kojima, H. Higuchi, Y. Harada, R. Vale, T. Funatsu, and T. Yanagida, “Multiple-molecule and single-molecule analysis of the actomyosin motor by nanometer piconewton manipulation with a microneedle: unitary steps and forces,” Biophys. J. 70, 383–400 (1996).
[CrossRef] [PubMed]

Ishiwata, S.

K. Kinosita, H. Itoh, S. Ishiwata, K. Hirano, T. Nishizaka, and T. Hayakawa, “Dual-view microscopy with a single camera: real-time imaging of molecular orientations and calcium,” J. Cell Biol. 115, 67–73 (1991).
[CrossRef] [PubMed]

Itoh, H.

K. Kinosita, H. Itoh, S. Ishiwata, K. Hirano, T. Nishizaka, and T. Hayakawa, “Dual-view microscopy with a single camera: real-time imaging of molecular orientations and calcium,” J. Cell Biol. 115, 67–73 (1991).
[CrossRef] [PubMed]

Jasny, J.

J. Sepiol, J. Jasny, J. Keller, and U. P. Wild, “Single molecules observed by immersion mirror objective: the orientation of terrylene molecules via the direction of its transition dipole-moment,” Chem. Phys. Lett. 273, 444–448 (1997).
[CrossRef]

J. Jasny and J. Sepiol, “Single molecules observed by immersion mirror objective: a novel method of finding the orientation of a radiating dipole,” Chem. Phys. Lett. 273, 439–443 (1997).
[CrossRef]

Jelezko, F.

C. Tietz, F. Jelezko, U. Gerken, S. Schuler, A. Schubert, H. Rogl, and J. Wrachtrup, “Single-molecule spectroscopy on the light-harvesting complex II of higher plants,” Biophys. J. 81, 556–562 (2001).
[CrossRef] [PubMed]

Keller, J.

J. Sepiol, J. Jasny, J. Keller, and U. P. Wild, “Single molecules observed by immersion mirror objective: the orientation of terrylene molecules via the direction of its transition dipole-moment,” Chem. Phys. Lett. 273, 444–448 (1997).
[CrossRef]

Keller, R. A.

W. P. Ambrose, P. M. Goodwin, J. C. Martin, and R. A. Keller, “Single-molecule detection and photochemistry of a surface using near-field optical excitation,” Phys. Rev. Lett. 72, 160–163 (1994).
[CrossRef] [PubMed]

Kennedy, G.

D. M. Warshaw, E. Hayes, D. Gaffney, A. M. Lauzon, J. R. Wu, G. Kennedy, K. Trybus, S. Lowey, and C. Berger, “Myosin conformational states determined by single fluorophore polarization,” Proc. Natl. Acad. Sci. (USA) 95, 8034–8039 (1998).
[CrossRef]

Kinosita, K.

K. Kinosita, “Real time imaging of rotating molecular machines,” FASEB J. 13, S201–S208 (1999).

K. Kinosita, “Linear and rotary molecular motors,” Adv. Exp. Med. Biol. 453, 5–14 (1998).
[CrossRef]

K. Kinosita, H. Itoh, S. Ishiwata, K. Hirano, T. Nishizaka, and T. Hayakawa, “Dual-view microscopy with a single camera: real-time imaging of molecular orientations and calcium,” J. Cell Biol. 115, 67–73 (1991).
[CrossRef] [PubMed]

Kojima, H.

A. Ishijima, H. Kojima, H. Higuchi, Y. Harada, R. Vale, T. Funatsu, and T. Yanagida, “Multiple-molecule and single-molecule analysis of the actomyosin motor by nanometer piconewton manipulation with a microneedle: unitary steps and forces,” Biophys. J. 70, 383–400 (1996).
[CrossRef] [PubMed]

Kuipers, L.

N. F. Van Hulst, J. A. Veerman, M. F. García-Parajó, and L. Kuipers, “Analysis of individual (macro)molecules and proteins using near-field optics,” J. Chem. Phys. 112, 7790–7810 (2000).
[CrossRef]

J. A. Veerman, M. F. Garcia-Parajo, L. Kuipers, and N. F. Van Hulst, “Single-molecule mapping of the optical field distribution of probes for near-field microscopy,” J. Microsc. (Oxford) 194, 477–482 (1999).
[CrossRef]

Laurence, T. A.

T. Ha, T. A. Laurence, D. S. Chemla, and S. Weiss, “Polarization spectroscopy of single fluorescent molecules,” J. Phys. Chem. B 103, 6839–6850 (1999).
[CrossRef]

Lauzon, A. M.

D. M. Warshaw, E. Hayes, D. Gaffney, A. M. Lauzon, J. R. Wu, G. Kennedy, K. Trybus, S. Lowey, and C. Berger, “Myosin conformational states determined by single fluorophore polarization,” Proc. Natl. Acad. Sci. (USA) 95, 8034–8039 (1998).
[CrossRef]

Levi, S. A.

J. A. Veerman, S. A. Levi, F. C. J. M. Van Veggel, D. N. Reinhoudt, and N. F. Van Hulst, “Near-field scanning optical microscopy of single fluorescent dendritic molecules,” J. Phys. Chem. A 103, 11264–11270 (1999).
[CrossRef]

Lieb, M. A.

Lowey, S.

D. M. Warshaw, E. Hayes, D. Gaffney, A. M. Lauzon, J. R. Wu, G. Kennedy, K. Trybus, S. Lowey, and C. Berger, “Myosin conformational states determined by single fluorophore polarization,” Proc. Natl. Acad. Sci. (USA) 95, 8034–8039 (1998).
[CrossRef]

Macklin, J. J.

J. K. Trautman and J. J. Macklin, “Time-resolved spectroscopy of single molecules using near-field and far-field optics,” Chem. Phys. 205, 221–229 (1996).
[CrossRef]

J. J. Macklin, J. K. Trautman, T. D. Harris, and L. E. Brus, “Imaging and time-resolved spectroscopy of single molecules at an interface,” Science 272, 255–258 (1996).
[CrossRef]

Martin, J. C.

W. P. Ambrose, P. M. Goodwin, J. C. Martin, and R. A. Keller, “Single-molecule detection and photochemistry of a surface using near-field optical excitation,” Phys. Rev. Lett. 72, 160–163 (1994).
[CrossRef] [PubMed]

Meixner, A. J.

M. A. Lieb and A. J. Meixner, “A high numerical aperture parabolic mirror as imaging device for confocal microscopy,” Opt. Express 8, 458–474 (2001), http://www.opticsexpress.org.
[CrossRef] [PubMed]

M. A. Bopp, A. J. Meixner, G. Tarrach, I. Zschokke-Gränacher, and L. Novotny, “Direct imaging of single molecule diffusion in a solid polymer host,” Chem. Phys. Lett. 263, 721–726 (1996).
[CrossRef]

Moerner, W. E.

R. M. Dickson, D. J. Norris, and W. E. Moerner, “Simultaneous imaging of individual molecules aligned both parallel and perpendicular to the optic axis,” Phys. Rev. Lett. 81, 5322–5325 (1998).
[CrossRef]

Montali, A.

W. Trabesinger, A. Renn, B. Hecht, U. P. Wild, A. Montali, P. Smith, and C. Weder, “Single-molecule imaging revealing the deformation-induced formation of a molecular polymer blend,” J. Phys. Chem. B 104, 5221–5224 (2000).
[CrossRef]

Nishizaka, T.

K. Kinosita, H. Itoh, S. Ishiwata, K. Hirano, T. Nishizaka, and T. Hayakawa, “Dual-view microscopy with a single camera: real-time imaging of molecular orientations and calcium,” J. Cell Biol. 115, 67–73 (1991).
[CrossRef] [PubMed]

Norris, D. J.

R. M. Dickson, D. J. Norris, and W. E. Moerner, “Simultaneous imaging of individual molecules aligned both parallel and perpendicular to the optic axis,” Phys. Rev. Lett. 81, 5322–5325 (1998).
[CrossRef]

Novotny, L.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86, 5251–5254 (2001).
[CrossRef] [PubMed]

B. Sick, B. Hecht, and L. Novotny, “Orientational imaging of single molecules by annular illumination,” Phys. Rev. Lett. 85, 4482–4485 (2000).
[CrossRef] [PubMed]

M. A. Bopp, A. J. Meixner, G. Tarrach, I. Zschokke-Gränacher, and L. Novotny, “Direct imaging of single molecule diffusion in a solid polymer host,” Chem. Phys. Lett. 263, 721–726 (1996).
[CrossRef]

Olson, C. E.

Peyser, L. A.

Previte, M. J. R.

Reinhoudt, D. N.

J. A. Veerman, S. A. Levi, F. C. J. M. Van Veggel, D. N. Reinhoudt, and N. F. Van Hulst, “Near-field scanning optical microscopy of single fluorescent dendritic molecules,” J. Phys. Chem. A 103, 11264–11270 (1999).
[CrossRef]

Renn, A.

W. Trabesinger, A. Renn, B. Hecht, U. P. Wild, A. Montali, P. Smith, and C. Weder, “Single-molecule imaging revealing the deformation-induced formation of a molecular polymer blend,” J. Phys. Chem. B 104, 5221–5224 (2000).
[CrossRef]

Richards, B.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London Ser. A 235, 358–379 (1959).
[CrossRef]

Rogl, H.

C. Tietz, F. Jelezko, U. Gerken, S. Schuler, A. Schubert, H. Rogl, and J. Wrachtrup, “Single-molecule spectroscopy on the light-harvesting complex II of higher plants,” Biophys. J. 81, 556–562 (2001).
[CrossRef] [PubMed]

Ruckstuhl, T.

Ruiter, A. G. T.

A. G. T. Ruiter, J. A. Veerman, M. F. Garcia-Parajo, and N. F. Van Hulst, “Single-molecule rotational and translational diffusion observed by near-field scanning optical microscopy,” J. Phys. Chem. A 101, 7318–7323 (1997).
[CrossRef]

Schryver, H. W.

J. Hofkens, W. Verheijen, R. Shulka, H. W. Schryver, and F. C. De, “Detection of a single dendrimer macromolecule with a fluorescent dihydropyrrolopurroledione (DPP) core embedded in a thin polystyrene film,” Macromolecules 32, 4493–4497 (1998).
[CrossRef]

Schubert, A.

C. Tietz, F. Jelezko, U. Gerken, S. Schuler, A. Schubert, H. Rogl, and J. Wrachtrup, “Single-molecule spectroscopy on the light-harvesting complex II of higher plants,” Biophys. J. 81, 556–562 (2001).
[CrossRef] [PubMed]

Schuler, S.

C. Tietz, F. Jelezko, U. Gerken, S. Schuler, A. Schubert, H. Rogl, and J. Wrachtrup, “Single-molecule spectroscopy on the light-harvesting complex II of higher plants,” Biophys. J. 81, 556–562 (2001).
[CrossRef] [PubMed]

Seeger, S.

Segers-Nolten, G. M. J.

M. F. Garcia-Parajo, J. A. Veerman, G. M. J. Segers-Nolten, B. G. De Grooth, J. Greve, and N. F. Van Hulst, “Visualizing individual green fluorescent proteins with a near-field optical microscope,” Cytometry 36, 239–246 (1999).
[CrossRef] [PubMed]

Selvin, P. R.

T. Ha, T. Enderle, D. S. Chemla, P. R. Selvin, and S. Weiss, “Single-molecule dynamics studied by polarization modulation,” Phys. Rev. Lett. 77, 3979–3982 (1996).
[CrossRef] [PubMed]

Sepiol, J.

J. Jasny and J. Sepiol, “Single molecules observed by immersion mirror objective: a novel method of finding the orientation of a radiating dipole,” Chem. Phys. Lett. 273, 439–443 (1997).
[CrossRef]

J. Sepiol, J. Jasny, J. Keller, and U. P. Wild, “Single molecules observed by immersion mirror objective: the orientation of terrylene molecules via the direction of its transition dipole-moment,” Chem. Phys. Lett. 273, 444–448 (1997).
[CrossRef]

Shulka, R.

J. Hofkens, W. Verheijen, R. Shulka, H. W. Schryver, and F. C. De, “Detection of a single dendrimer macromolecule with a fluorescent dihydropyrrolopurroledione (DPP) core embedded in a thin polystyrene film,” Macromolecules 32, 4493–4497 (1998).
[CrossRef]

Sick, B.

B. Sick, B. Hecht, and L. Novotny, “Orientational imaging of single molecules by annular illumination,” Phys. Rev. Lett. 85, 4482–4485 (2000).
[CrossRef] [PubMed]

Smith, P.

W. Trabesinger, A. Renn, B. Hecht, U. P. Wild, A. Montali, P. Smith, and C. Weder, “Single-molecule imaging revealing the deformation-induced formation of a molecular polymer blend,” J. Phys. Chem. B 104, 5221–5224 (2000).
[CrossRef]

So, P. T. C.

Tarrach, G.

M. A. Bopp, A. J. Meixner, G. Tarrach, I. Zschokke-Gränacher, and L. Novotny, “Direct imaging of single molecule diffusion in a solid polymer host,” Chem. Phys. Lett. 263, 721–726 (1996).
[CrossRef]

Tietz, C.

C. Tietz, F. Jelezko, U. Gerken, S. Schuler, A. Schubert, H. Rogl, and J. Wrachtrup, “Single-molecule spectroscopy on the light-harvesting complex II of higher plants,” Biophys. J. 81, 556–562 (2001).
[CrossRef] [PubMed]

Trabesinger, W.

W. Trabesinger, A. Renn, B. Hecht, U. P. Wild, A. Montali, P. Smith, and C. Weder, “Single-molecule imaging revealing the deformation-induced formation of a molecular polymer blend,” J. Phys. Chem. B 104, 5221–5224 (2000).
[CrossRef]

Trautman, J. K.

J. J. Macklin, J. K. Trautman, T. D. Harris, and L. E. Brus, “Imaging and time-resolved spectroscopy of single molecules at an interface,” Science 272, 255–258 (1996).
[CrossRef]

J. K. Trautman and J. J. Macklin, “Time-resolved spectroscopy of single molecules using near-field and far-field optics,” Chem. Phys. 205, 221–229 (1996).
[CrossRef]

Trybus, K.

D. M. Warshaw, E. Hayes, D. Gaffney, A. M. Lauzon, J. R. Wu, G. Kennedy, K. Trybus, S. Lowey, and C. Berger, “Myosin conformational states determined by single fluorophore polarization,” Proc. Natl. Acad. Sci. (USA) 95, 8034–8039 (1998).
[CrossRef]

Vale, R.

A. Ishijima, H. Kojima, H. Higuchi, Y. Harada, R. Vale, T. Funatsu, and T. Yanagida, “Multiple-molecule and single-molecule analysis of the actomyosin motor by nanometer piconewton manipulation with a microneedle: unitary steps and forces,” Biophys. J. 70, 383–400 (1996).
[CrossRef] [PubMed]

Van den Bout, D. A.

L. A. Deschenes and D. A. Van den Bout, “Single-molecule studies of heterogeneous dynamics in polymer melts near the glass transition,” Science 292, 233–234 (2001).
[CrossRef]

Van Hulst, N. F.

N. F. Van Hulst, J. A. Veerman, M. F. García-Parajó, and L. Kuipers, “Analysis of individual (macro)molecules and proteins using near-field optics,” J. Chem. Phys. 112, 7790–7810 (2000).
[CrossRef]

J. A. Veerman, S. A. Levi, F. C. J. M. Van Veggel, D. N. Reinhoudt, and N. F. Van Hulst, “Near-field scanning optical microscopy of single fluorescent dendritic molecules,” J. Phys. Chem. A 103, 11264–11270 (1999).
[CrossRef]

J. A. Veerman, M. F. Garcia-Parajo, L. Kuipers, and N. F. Van Hulst, “Single-molecule mapping of the optical field distribution of probes for near-field microscopy,” J. Microsc. (Oxford) 194, 477–482 (1999).
[CrossRef]

M. F. Garcia-Parajo, J. A. Veerman, G. M. J. Segers-Nolten, B. G. De Grooth, J. Greve, and N. F. Van Hulst, “Visualizing individual green fluorescent proteins with a near-field optical microscope,” Cytometry 36, 239–246 (1999).
[CrossRef] [PubMed]

A. G. T. Ruiter, J. A. Veerman, M. F. Garcia-Parajo, and N. F. Van Hulst, “Single-molecule rotational and translational diffusion observed by near-field scanning optical microscopy,” J. Phys. Chem. A 101, 7318–7323 (1997).
[CrossRef]

Van Veggel, F. C. J. M.

J. A. Veerman, S. A. Levi, F. C. J. M. Van Veggel, D. N. Reinhoudt, and N. F. Van Hulst, “Near-field scanning optical microscopy of single fluorescent dendritic molecules,” J. Phys. Chem. A 103, 11264–11270 (1999).
[CrossRef]

Veerman, J. A.

N. F. Van Hulst, J. A. Veerman, M. F. García-Parajó, and L. Kuipers, “Analysis of individual (macro)molecules and proteins using near-field optics,” J. Chem. Phys. 112, 7790–7810 (2000).
[CrossRef]

J. A. Veerman, S. A. Levi, F. C. J. M. Van Veggel, D. N. Reinhoudt, and N. F. Van Hulst, “Near-field scanning optical microscopy of single fluorescent dendritic molecules,” J. Phys. Chem. A 103, 11264–11270 (1999).
[CrossRef]

J. A. Veerman, M. F. Garcia-Parajo, L. Kuipers, and N. F. Van Hulst, “Single-molecule mapping of the optical field distribution of probes for near-field microscopy,” J. Microsc. (Oxford) 194, 477–482 (1999).
[CrossRef]

M. F. Garcia-Parajo, J. A. Veerman, G. M. J. Segers-Nolten, B. G. De Grooth, J. Greve, and N. F. Van Hulst, “Visualizing individual green fluorescent proteins with a near-field optical microscope,” Cytometry 36, 239–246 (1999).
[CrossRef] [PubMed]

A. G. T. Ruiter, J. A. Veerman, M. F. Garcia-Parajo, and N. F. Van Hulst, “Single-molecule rotational and translational diffusion observed by near-field scanning optical microscopy,” J. Phys. Chem. A 101, 7318–7323 (1997).
[CrossRef]

Verheijen, W.

J. Hofkens, W. Verheijen, R. Shulka, H. W. Schryver, and F. C. De, “Detection of a single dendrimer macromolecule with a fluorescent dihydropyrrolopurroledione (DPP) core embedded in a thin polystyrene film,” Macromolecules 32, 4493–4497 (1998).
[CrossRef]

Warshaw, D. M.

D. M. Warshaw, E. Hayes, D. Gaffney, A. M. Lauzon, J. R. Wu, G. Kennedy, K. Trybus, S. Lowey, and C. Berger, “Myosin conformational states determined by single fluorophore polarization,” Proc. Natl. Acad. Sci. (USA) 95, 8034–8039 (1998).
[CrossRef]

Weder, C.

W. Trabesinger, A. Renn, B. Hecht, U. P. Wild, A. Montali, P. Smith, and C. Weder, “Single-molecule imaging revealing the deformation-induced formation of a molecular polymer blend,” J. Phys. Chem. B 104, 5221–5224 (2000).
[CrossRef]

Weiss, S.

T. Ha, T. A. Laurence, D. S. Chemla, and S. Weiss, “Polarization spectroscopy of single fluorescent molecules,” J. Phys. Chem. B 103, 6839–6850 (1999).
[CrossRef]

T. Ha, T. Enderle, D. S. Chemla, and S. Weiss, “Dual-molecule spectroscopy: molecular rulers for the study of biological macromolecules,” IEEE J. Sel. Top. Quantum Electron. 2, 1115–1128 (1996).
[CrossRef]

T. Ha, T. Enderle, D. S. Chemla, P. R. Selvin, and S. Weiss, “Single-molecule dynamics studied by polarization modulation,” Phys. Rev. Lett. 77, 3979–3982 (1996).
[CrossRef] [PubMed]

Wild, U. P.

W. Trabesinger, A. Renn, B. Hecht, U. P. Wild, A. Montali, P. Smith, and C. Weder, “Single-molecule imaging revealing the deformation-induced formation of a molecular polymer blend,” J. Phys. Chem. B 104, 5221–5224 (2000).
[CrossRef]

J. Sepiol, J. Jasny, J. Keller, and U. P. Wild, “Single molecules observed by immersion mirror objective: the orientation of terrylene molecules via the direction of its transition dipole-moment,” Chem. Phys. Lett. 273, 444–448 (1997).
[CrossRef]

Wolf, E.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London Ser. A 235, 358–379 (1959).
[CrossRef]

Wrachtrup, J.

C. Tietz, F. Jelezko, U. Gerken, S. Schuler, A. Schubert, H. Rogl, and J. Wrachtrup, “Single-molecule spectroscopy on the light-harvesting complex II of higher plants,” Biophys. J. 81, 556–562 (2001).
[CrossRef] [PubMed]

Wu, J. R.

D. M. Warshaw, E. Hayes, D. Gaffney, A. M. Lauzon, J. R. Wu, G. Kennedy, K. Trybus, S. Lowey, and C. Berger, “Myosin conformational states determined by single fluorophore polarization,” Proc. Natl. Acad. Sci. (USA) 95, 8034–8039 (1998).
[CrossRef]

Yanagida, T.

A. Ishijima, H. Kojima, H. Higuchi, Y. Harada, R. Vale, T. Funatsu, and T. Yanagida, “Multiple-molecule and single-molecule analysis of the actomyosin motor by nanometer piconewton manipulation with a microneedle: unitary steps and forces,” Biophys. J. 70, 383–400 (1996).
[CrossRef] [PubMed]

Youngworth, K. S.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86, 5251–5254 (2001).
[CrossRef] [PubMed]

Zschokke-Gränacher, I.

M. A. Bopp, A. J. Meixner, G. Tarrach, I. Zschokke-Gränacher, and L. Novotny, “Direct imaging of single molecule diffusion in a solid polymer host,” Chem. Phys. Lett. 263, 721–726 (1996).
[CrossRef]

Adv. Exp. Med. Biol. (1)

K. Kinosita, “Linear and rotary molecular motors,” Adv. Exp. Med. Biol. 453, 5–14 (1998).
[CrossRef]

Appl. Opt. (1)

Biophys. J. (2)

A. Ishijima, H. Kojima, H. Higuchi, Y. Harada, R. Vale, T. Funatsu, and T. Yanagida, “Multiple-molecule and single-molecule analysis of the actomyosin motor by nanometer piconewton manipulation with a microneedle: unitary steps and forces,” Biophys. J. 70, 383–400 (1996).
[CrossRef] [PubMed]

C. Tietz, F. Jelezko, U. Gerken, S. Schuler, A. Schubert, H. Rogl, and J. Wrachtrup, “Single-molecule spectroscopy on the light-harvesting complex II of higher plants,” Biophys. J. 81, 556–562 (2001).
[CrossRef] [PubMed]

Chem. Phys. (1)

J. K. Trautman and J. J. Macklin, “Time-resolved spectroscopy of single molecules using near-field and far-field optics,” Chem. Phys. 205, 221–229 (1996).
[CrossRef]

Chem. Phys. Lett. (3)

M. A. Bopp, A. J. Meixner, G. Tarrach, I. Zschokke-Gränacher, and L. Novotny, “Direct imaging of single molecule diffusion in a solid polymer host,” Chem. Phys. Lett. 263, 721–726 (1996).
[CrossRef]

J. Jasny and J. Sepiol, “Single molecules observed by immersion mirror objective: a novel method of finding the orientation of a radiating dipole,” Chem. Phys. Lett. 273, 439–443 (1997).
[CrossRef]

J. Sepiol, J. Jasny, J. Keller, and U. P. Wild, “Single molecules observed by immersion mirror objective: the orientation of terrylene molecules via the direction of its transition dipole-moment,” Chem. Phys. Lett. 273, 444–448 (1997).
[CrossRef]

Cytometry (1)

M. F. Garcia-Parajo, J. A. Veerman, G. M. J. Segers-Nolten, B. G. De Grooth, J. Greve, and N. F. Van Hulst, “Visualizing individual green fluorescent proteins with a near-field optical microscope,” Cytometry 36, 239–246 (1999).
[CrossRef] [PubMed]

FASEB J. (1)

K. Kinosita, “Real time imaging of rotating molecular machines,” FASEB J. 13, S201–S208 (1999).

IEEE J. Sel. Top. Quantum Electron. (1)

T. Ha, T. Enderle, D. S. Chemla, and S. Weiss, “Dual-molecule spectroscopy: molecular rulers for the study of biological macromolecules,” IEEE J. Sel. Top. Quantum Electron. 2, 1115–1128 (1996).
[CrossRef]

J. Cell Biol. (1)

K. Kinosita, H. Itoh, S. Ishiwata, K. Hirano, T. Nishizaka, and T. Hayakawa, “Dual-view microscopy with a single camera: real-time imaging of molecular orientations and calcium,” J. Cell Biol. 115, 67–73 (1991).
[CrossRef] [PubMed]

J. Chem. Phys. (1)

N. F. Van Hulst, J. A. Veerman, M. F. García-Parajó, and L. Kuipers, “Analysis of individual (macro)molecules and proteins using near-field optics,” J. Chem. Phys. 112, 7790–7810 (2000).
[CrossRef]

J. Microsc. (Oxford) (1)

J. A. Veerman, M. F. Garcia-Parajo, L. Kuipers, and N. F. Van Hulst, “Single-molecule mapping of the optical field distribution of probes for near-field microscopy,” J. Microsc. (Oxford) 194, 477–482 (1999).
[CrossRef]

J. Opt. Soc. Am. B (1)

J. Phys. Chem. A (2)

A. G. T. Ruiter, J. A. Veerman, M. F. Garcia-Parajo, and N. F. Van Hulst, “Single-molecule rotational and translational diffusion observed by near-field scanning optical microscopy,” J. Phys. Chem. A 101, 7318–7323 (1997).
[CrossRef]

J. A. Veerman, S. A. Levi, F. C. J. M. Van Veggel, D. N. Reinhoudt, and N. F. Van Hulst, “Near-field scanning optical microscopy of single fluorescent dendritic molecules,” J. Phys. Chem. A 103, 11264–11270 (1999).
[CrossRef]

J. Phys. Chem. B (4)

W. Trabesinger, A. Renn, B. Hecht, U. P. Wild, A. Montali, P. Smith, and C. Weder, “Single-molecule imaging revealing the deformation-induced formation of a molecular polymer blend,” J. Phys. Chem. B 104, 5221–5224 (2000).
[CrossRef]

A. P. Bartko and R. M. Dickson, “Three-dimensional orientations of polymer-bound single molecules,” J. Phys. Chem. B 103, 3053–3056 (1999).
[CrossRef]

A. P. Bartko and R. M. Dickson, “Imaging three-dimensional single-molecule orientations,” J. Phys. Chem. B 103, 11237–11241 (1999).
[CrossRef]

T. Ha, T. A. Laurence, D. S. Chemla, and S. Weiss, “Polarization spectroscopy of single fluorescent molecules,” J. Phys. Chem. B 103, 6839–6850 (1999).
[CrossRef]

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[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Geometry of the dipole emission above an interface. The dipole emission can be thought of as a superposition of plane waves, each with a specific polarization and amplitude. At the interface, each of these plane-wave components is reflected and transmitted. The complete emission into the lower dielectric is given by the superposition of the transmitted plane waves.

Fig. 2
Fig. 2

Geometry of the imaging from the interface onto the CCD camera. The camera is positioned directly in the design image plane of the optics. For ideally aplanatic optics, a spherical wave front of a point source at the focus of the optics in object space is converted into a spherical wave front converging toward the conjugated focus in image space.

Fig. 3
Fig. 3

Detected images of single Cy5 molecules deposited upon glass in air at a defocusing value of -1 μm (displacement of the objective toward the sample).

Fig. 4
Fig. 4

Comparison of, left to right, measured images of a single molecule and theoretically calculated images for three different dipole orientations as marked and for the defocusing values indicated at the left. The white scale bars have a length of 100 μm. The correspondence between intensity and gray value is shown by the gray scale at the bottom. The calculations were made for a 1.4-N.A. oil immersion objective with 60× magnification imaging dipoles at an air–glass interface.

Equations (22)

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E=ik022πdqw0 [epTp(e0pp)+esTs(esp)]×exp[iq(ρ-ρ0)+iw0|z0|+iwz].
e0,p=(cos ψ cos η0, sin ψ cos η0, -sin η0),
ep=(cos ψ cos η, sin ψ cos η, -sin η),
es=(-sin ψ, cos ψ,0);
Ep(η)=epEp(η)=-epnwqnmwm Tpexp(iwm|zm|),
epEp(η)cos ψ=epnwnm Tpexp(iwm|zm|)cos ψ,
esEs(η)sin ψ=-esnwwm Tsexp(iwm|zm|)sin ψ.
E=M ΩdΩncos ηn cos η1/2epEpexp(iksr+ikδz cos η),
B=MnΩdΩncos ηn cos η1/2esEpexp(iksr+ikδz cos η),
ep=(cos ψ cos η, sin ψ cos η, -sin η),
s=(-cos ψ sin η, -sin ψ sin η, cos η).
E=M ΩdΩncos ηn cos η1/2(epEpcos ψ+esEssin ψ)exp(iksr+ikδz cos η),
B=MnΩdΩncos ηn cos η1/2(e^sEpcos ψ-epEssin ψ)exp(iksr+ikδz cos η).
sr=s(R+ρ+z)=R-ρsin ηcos(ψ-ϕ)+zcos η,
EjBj=M0ηmaxdηsin ηncos ηn cos η1/2ejbj×exp(ikzcos η+ikδz cos η),
exey=i cos ηJ1Epcos ϕsin ϕ,
bxby=inJ1Ep-sin ϕcos ϕ,
exey=i2  
×cos η(J0-J2cos 2ϕ)Ep+(J0+J2cos 2ϕ)Es-cos ηJ2sin 2ϕEp+J2sin 2ϕEs,
bxby=in2  
×-cos ηJ2sin 2ϕEs+J2sin 2ϕEp  cos η(J0+J2cos 2ϕ)Es+(J0-J2cos 2ϕ)Ep.
S=(c/8π)ez(E×B*),

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